This thesis demonstrates how a Taylor rule could capture the monetary policy decision pro-

Abstract.

This thesis demonstrates how a Taylor rule could capture the monetary policy decision pro-

cess with imperfect information. The changes in the weights present in the rule refect policy

regime shifts. This framework is suitable in studying a small open transitional economy such

as Hungary in recent years. This thesis employs the State-Space model which may capture

the time-varying weights in the Taylor rule and an Autoregressive Hidden Markov Model

which may identify unobservable or hidden underlying regimes using structural breaks. This

thesis employs a sample period from 2000Q1-2020Q2, which fnds that an active monetary

policy regime transitions to a passive regime which becomes dominant in the second half

of the sample, namely from 2014Q1 onward. Additionally, evidence of ine˙ective monetary

policy is found. As general evidence, this thesis fnds support for the Taylor rule constructed

through the partial use of intermediate policy targets such as the real e˙ective exchange

rate. Which becomes ine˙ective towards the end of the sample, as the nominal interest rate

degrades from two percent towards the zero lower bound.

Contents

Abstract. 3

1 Introduction. 6

1,1 Problem statement. . . 7

1,2 Purpose. . . 8

1,3 Research question: . . . 9

2 Literature Review. 10 3 Theoretical Framework. 13 3,1 Capital mobility and nominal interest rate parity. . . . 13

3,2 The AS-AD framework. . . . 14

3,3 Central bank loss function with limited information. . . 18

3,4 The Taylor Rule and the Lucas critique. . . . 19

4 Methodologies & Data. 21 4,1 Time-varying state-space model. . . 21

4,2 The Kalman Filter. . . 22

4,3 Autoregressive Hidden Markov Switching model. . . 24

4,4 Data collection and management. . . . 25

4,5 Autoregressive Hidden Markov Model. . . . 28

4,6 State-Space Model. . . 29

5 Empirical Results & Discussion 30 5,1 Empirical Results . . . 30

5,2 Empirical Discussion. . . 36

6 Concluding Remarks. 41

7 References 43

Appendix 47

1 Introduction.

Macroeconomic stability is historically not commonly associated with central European economies, the most obvious being the infationary example of the Weimar Republic of Germany during the interwar years. Continental and especially Central/Eastern Europe has been the melting pot for important economic and political events throughout the twentieth century. Two world wars and powerful clashes between political and economic systems have rocked the macroeconomic stability of emerging economies in Central Europe and helped shape what can be observed today.

One signifcant part of the rapidly growing emerging economies in central Europe is Hungary, the third largest of the Visegrad Group (or V4). A nation which su˙ered tremendously due to the Trianon Treaty, losing nearly 75% of its territories, more than half its populace and forced to pay massive reparations to foreign powers during the frst half of the century (Britannica, 2020). The following decades of Soviet occupation after the Axis defeat in 1945, which stripped the country of its resources, decimated its infrastructure and instituted heavy industries with no regard for domestic Hungarian needs or suitability for production.

After the revolution of 1956 Hungary slowly regained its independence and began market and economic reforms, including restructuring of the banking system, which would not gain any real e˙ect until the 1980s. However, the spirit of economic development continued with increased privatizations, initiatives for voluntary export and trade with Hungary’s neighbours and new found post war allies.

With low output growth and high infation being present for the majority of the post revo- lutionary Hungarian republic, the importance of trade and economic aid, with guidance for economic development was essential. Transitioning from a planned economy to a market economy aided in providing the means of remedying the problems created by the former.

Since the introduction of further economic policies in the 1980s, the GDP growth per capita

in Hungary increased signifcantly, with gradual disinfation to accompany it.

Obviously, the restructuring of the Hungarian economy has proved successful compared to the previous predicament of reversed fow of output growth and price levels. This creates an opportunity to descriptively explore how this gradual successful transition was achieved, through regime oriented economic theory and application. Not only for the advancement of understanding the particular situation of Hungary, but to further generate knowledge that may aid the development of other economies in similar or comparable stages of development today or in the future.

During the early 2000s, the central bank of Hungary (Magyar Nemzeti Bank or MNB) enjoyed a dual goal of maintaining price stability along a semi-fxed exchange rate to the Euro, with infation targeting adopted in 2001 (MNB, 2020). However, in 2008 the MNB and the Hungarian government elected to let the exchange rate foat, in favour of only maintaining price stability by explicit infation targeting (MNB, 2020). It was also decided that management of the exchange rate is to be in accordance with both the government and the monetary council presiding over MNB. This commitment to price stability provides a point of inquiry examining how regimes with potential implicit goals of monetary policy by the MNB can be detected. Considering that potential conficting aspects of monetary policy parameters may impact di˙ering unobservable or hidden regimes/regime shifts to be identifed.

1,1 Problem statement.

The feasible goals of monetary authorities is usually characterized by macroeconomic stabil-

ity at or close to desired levels of infation, output and unemployment among other important

variables. Aside from the long run equilibrium of economic theory, these indicators are rarely

at the desired levels of the monetary authorities in the economy and become more compli-

cated as international trade impacts the stability of individual economies. Macroeconomic

instability is therefore an important point of study both in evaluation of monetary policy

regimes ex post in order to evaluate its real e˙ects contra the desired e˙ect in an e˙ort to

improve future macroeconomic stability in both developed and emerging economies which

may employ similar instruments and/or goals.

The economist John B Taylor (Taylor, 1993) attempted to describe how monetary authori- ties could achieve macroeconomic stability for a closed economy, with considerations to a set of minimalist economic indicators measured ex post. These indicators assume that the mon- etary authorities practices active monitoring of domestic economic conditions and employs some degree of infation targeting. Creating a simple rule for monetary authorities to deter- mine the level of the nominal interest rate, which Taylor perceived as the main instrument of monetary authorities for regulating and achieving macroeconomic stability.

Below is the traditional Taylor rule constructed by Taylor in 1993, without a lagged nominal interest rate which were added in his 1999 revision.

i

= r + a(ˇ

− ˇ

) + b(y

− y

) (eq I)

The weights proposed by Taylor (a) and (b) originally equal 0, 5 but were reevaluated in an attempt to prove that given an objective function of the central bank, the rule is actually an optimal one (weights now equal to (a = 1, 5) and (b = 1), Taylor, 1999). This reexamination also provided what became known as the Taylor principle; employing a weight of (a > 1) will stabilize the macroeconomy with a more than one-to-one ratio of the nominal interest rate, creating a rise in the real interest rate dampening infationary tendencies and slowing the economy (Ibid). Sizes of empirically estimated weights would indicate how active a given regime is in this framework.

Since Taylors original publication, criticism regarding potential underlying regimes and as- sumptions of application of Taylor type monetary policy rules have been debated. Di˙er- ent regimes may exist set on prioritizing one macroeconomic variable present in the Tay- lor/monetary policy rules, e.g. preferences for output targeting alongside price stability tar- geting (recession avoidance) may contradict the explicit policy goal.

1,2 Purpose.

This rule provides the outset from which this thesis aims to describe the modern historical

monetary policies enacted by the MNB for the purpose of achieving its defned objective

by the use of a modifed rendition of the Taylor rule ex post. Expanding the traditional

Taylor rule to capture additional macroeconomic factors determinant in explaining past regimes/regime shifts of monetary policy by the MNB. To augment and expand previous research in the feld with additional data and estimates through a regime oriented methodol- ogy and empirical discussion, including the abnormal situation now facing many economies with ine˙ective monetary policy. Lastly, it aims to identify and describe a Hidden Markov Model that describes regimes and regime shifts in monetary policy in Hungary during the sample period ex post.

1,3 Research question:

Given the stated objective of monetary policy established by the central bank of Hungary and the e˙orts exhausted to obtain that objective, is it possible using an extended rendition of the Taylor rule to accurately describe regimes/regime shifts of monetary policy ex post?

The sample period examined ranges from the year 2000 quarter one until 2020 quarter two,

with data corresponding to eighty two observations per variable vector. Thus, the sample

period envelops both the global events of The Great Recession (plagued by low infation and

risk of defation) and partially the lockdowns of 2019-2020. Representing two immensely

important time periods in the forum of economics and fnancial analysis respectively.

2 Literature Review.

Applications of Taylor type rules in small open economies typically beneft from expansion of the original Taylor rule. Both Österholm (2005), Balabay (2011) and Tarkhan-Mouravi (2009) apply the real e˙ective exchange rate as a weighted index to extend the reaction function of the monetary policy transmission mechanism. This addition is further supported by the theoretical estimation exercise conducted by Svensson (2000), which fnds that the transmission mechanism of the interest rate is greatly signifcant in a˙ecting the real e˙ec- tive exchange rate in Taylor type rules. Frömmel and Schobert (2006) fnds that emerging economies in former soviet Eastern Europe exhibit a “fear of foating”, with evidence of both explicit and implicit exchange rate targeting with either none or contradictory monetary policy goals. Emphasizing the importance of exchange rate policy shifts in monetary policy during sample periods.

Application in a UK study, Nelson (2001) considered the Taylor rule performance during the period ex ante and ex post ERM, with support for the Taylor rule after emergence from ERM e˙ectively moving from exchange rate targeting to infation targeting. Christiano and Ros- tagno (2001) fnds that not only does estimated Taylor type rules show signs of non-linearity, but also the possibility for multiple equilibria. Conditional on the current infation (unique equilibria) or future infation (multiple equilibria) is used for measurement. The multiple equilibria argument is supported by Benhabib, Schmitt-Grohe and Uribe (1999), emphasizing both model specifcation concerns and possible misinterpretation by economists. Benhabib, Schmitt-Grohe and Uribe exemplifes this by describing attempts made to estimate a slope of infation around a steady state in the area which monetary policy is active, leading to a conclusion that monetary policy has always been active despite underlying evidence to the contrary.

Woodford (2001) argues that the output gap itself may not be linear and that using the

detrended output for estimation of the output gap provides a poor explanatory account of

infation. Alternatively, Woodford argues that usage of the marginal cost of real unit labour,

as the cost price ratio determines deadweight loss and incentives to raise prices, possess

signifcant explanatory power of medium frequency variation in infation.

In contrast Judd, Rudebusch (1998) follows a similar construction of the potential output component of the output gap as the US federal reserve, with a time-varying natural rate of unemployment (NAIRU) in the context of a Phillips curve. Assuming a structural approach considering the output gap and its relationship with future infation. Orphanides (2002 &

2003) considers the GDP defator used by Taylor (1993) as an inappropriate measure of infation, since such information is unavailable to policy makers ex ante. Orphanides also o˙ers a growth rule alternative to the traditional Taylor type rule, targeting “growth” of nominal income. Avoiding the pitfalls of natural-rate-gap policies, relying on the lagged value of the interest rate instrument for policy adjustment (
i) rather than (i). Cukierman (2008) highlights the risk of preferences of positive versus negative gaps of infation and output to the monetary authorities.

Other approaches regarding the interest rate in Taylor type rules are examined by Svens- son (2000 & 2003), Nelson (2001), Frömmel and Schobert (2006) who employ interest rate smoothing, central banks maintain momentum when adjusting monetary policy. However, there is no consensus in this issue. Similar objections to traditional specifcations are raised by Gerlach-Kristen (2003) regarding a possibly non constant infation target. Suggesting that if the basis for the infation target is rooted in the expectation hypothesis, the target assumption is not empirically valid.

Gerlach-Kristen (2003) show that traditional Taylor rules forecast poorly out of sample, presenting an alternative estimation with explicit considerations to non-stationarity. Or- phanides (2002 & 2003) is concerned with both the information set available to monetary policy makers, as accurate “current” information is not available until ex post. Orphanides exemplifes the defnitions of “potential” and “normal” as signifcant to policy makers given the information available ex ante versus ex post, when implementing monetary policy. Clar- ida, Gali, Gertler (1998) using a GMM estimation fnds that the Bundesbank responds to anticipated infation rather than lagged, supporting central bank forward-looking behaviour.

It is also supported in the Euro area by Gerlach, Kristen (2003) who fnds that using the real

interest rate in the short run captures the long run relationship more appropriately, again

suggesting a forward-looking central bank.

Svensson (2003) examines both forward and backward-looking models of Taylor type rules, fnding support for both types of perspectives dependent on the specifc rule used (instrument or targeting rule).

Christiano and Rostagno (2001) emphasizes through a cash-credit model the importance of fscal policy in relation to monetary policy, with descriptions of household, frms, mon- etary and fscal authorities. They argue, that as governments must maintain solvency on government debt but not liabilities, as a liquidity trap cannot constitute an equilibrium out- come in monetary policy. Nelson (2001) likewise examines the complementation of fscal and monetary policies, where income policies, food subsidies and cuts in indirect taxation are considered in attempts to control infation during the ERM period of the UK.

Orphanides (2003) fnds that reduced monetary policy activism has been consistent with more preferable outcomes since the Great Infation, with some support from Svensson (2000) who argues that fexible infation targeting is more e˙ective and provides less room for ac- tivism compared to strict infation targeting. Benhabib, Schmitt-Grohe and Uribe (1999) fnds that active monetary policy near the infation target increases risk of defation, com- pared to passive monetary policy through e.g. interest rate or exchange rate peg.

Regime shifting models are common when examining relationships between monetary policy

parameters. Hoshikawa (2011), employs a regime shifting model to examine Japanese foreign

exchange policy, fnding a long term relationship between foreign currency reserves and the

YEN/USD exchange rate. Reschreiter (2010) fnds that a monetary policy regime shift

from exchange rate targeting to infation targeting through the real interest rate occurs in

the UK, after the exit from ERM with a time-varying mean-reverting framework. Ibrahim

Arısoy (2013) instead uses the Kalman flter for regime shifts using the Fisher equation in

Turkey, with limited support for the Fisher hypothesis.

3 Theoretical Framework.

This section aims to describe and discuss the theoretical aspects of monetary policy and what parameters might contribute to changes in monetary policy regimes. Based on the framework developed by Friedman and Keynes respectively, as described by Sorensen &

Jacobsen (2010).

3,1 Capital mobility and nominal interest rate parity.

In an open economy with interactive capital and goods markets, any arbitrage opportunities presented by di˙ering yields of assets will generate capital mobility. This would be prob- lematic since large in and outfows of capital will a˙ect output and infation in both sender and recipient countries respectively. Given that capital mobility is perfect, nominal interest rates of open economies must present equal yields for such arbitrage opportunities to be rare or non existent, this can be formalized by the following condition known as the uncovered interest rate parity (UIP):

(1 + i) = (1 + i

)(

) (eq I)

Where (i) = the domestic nominal interest rate, (i

) = the foreign nominal interest rate, (E) = nominal exchange rate and (E

) = nominal exchange rate expected to prevail in the next period.

This conditions states that an investor can either invest domestically and earn (1+i) amount of wealth in the current period (ignoring Fx forwards) or alternatively purchase (

) units of foreign currency giving an amount of wealth equal to (

)(1 + i

) in foreign currency. In simple terms, foreign and domestic investments must yield the same end-of-period wealth and thus have the same expected rate of return.

Taking the logs of both sides of this condition, where (lnx ˇ x) gives the approximate condition of:

i = i

+ e

− e -> e

= lnE

(eq II, III)

The frst equation shows that if the domestic currency is expected to depreciate in the next

period, the domestic nominal interest must rise to maintain interest rate parity. This would of course imply that the central bank defends a fxed exchange rate. However, by allowing the domestic exchange rate to adjust to di˙erences in the nominal interest rate, parity can be maintained with capital mobility with the central bank setting the nominal interest rate according to other monetary goals.

Assuming that small open economies maintain infation targets similar to each other to achieve macroeconomic stability and successfully attain this goal in the long term, it can be postulated that:

ˇ

= ˇ

->
e = e − e

(eq IV, V)

The nominal exchange rate itself cannot serve as a nominal anchor for infation given an open economy, but interest rate parity CAN be maintained by allowing the exchange rate to adjust. And by maintaining domestic infation equal or close to foreign infation the nominal exchange rate can remain stable. This means that appreciation and depreciation between currencies can be kept stable and minimize large changes in net-export.

3,2 The AS-AD framework.

Assuming that the central bank sets its nominal interest rate in advance of observed shocks, is aware of the existence of an AD function which include demand shocks, where said shocks cannot be observed directly and that the monetary policy regime does not attempt to obtain output levels above the natural rate. A domestic goods market equilibrium that can be represented by:

(y

− y) = z

− a

(i

− ˇ

− r

) (eq VI) Where (z

) contains unobservable demand shocks for the next period, (i) = nominal in- terest rate and (r

) = risk free steady-state real interest rate. This also implicitly assumes that the central bank has a structural understanding of the open economy in question and that expectations are static (backward-looking). Furthermore, the AS function is given by:

ˇ

= ˇ

+ (y

− y) + S

(eq VII)

With the term (S

) containing supply shocks for future periods.

Given this model for market equilibrium in conjunction with the UIP means that monetary policy regimes will have to satisfy both equilibrium conditions in the long run for any regime to be stable. For the goods market equilibrium to hold for an small open economy, any di˙erences in future and natural output has to be balanced by either net-export or fnancial fows such as savings and investments, which is then a˙ected by the UIP condition.

Consider an open economy with perfect capital mobility and with a central bank that pursue a fxed exchange rate regime. This encompasses several types of monetary policy regimes ranging from a completely fxed nominal exchange rate (or hard peg) to a relatively fexible exchange rate bandwidth (soft peg).

Given the UIP (I) described above fxing the nominal exchange rate would imply that:

e

− e = 0 thus i = i

And the real exchange rate is given by:

= (

E

) (eq VIII)

Implies that the change in the real exchange rate is given by:

(e

− e

) = (ˇ

− ˇ) (eq IX)

e = lnE

ˇ

= (lnP

− lnP

) = (lnP − lnP

) (eq X) Domestic infation must then correspond to foreign infation if the real exchange rate is to remain stable in the long term equilibrium. Any domestic infation deviation from foreign infation will be refected in the real exchange rate forcing a response from the central bank.

Which must, in order to defend the fxed exchange rate, adjust its nominal interest rate.

Should the central bank allow the domestic nominal interest rate to be below the foreign nominal interest rate, it would need to deplete its own foreign currency reserves to combat the outfow of capital when investors sell massive amounts of domestic currency and purchase foreign currency which the central bank must facilitate.

Should the domestic nominal interest rate be higher than the foreign nominal interest rate,

it would result in a massive infow of capital and domestic infationary pressure with a rising

nominal exchange rate. Regardless of what type of fxed/bandwidth exchange rate regime is adopted, the central bank can no longer pursue independent monetary policy to regulate the domestic economy without considering the e˙ects on the domestic nominal exchange rate.

If this monetary policy regime is credible to agents in the market any expected and actual change in the exchange rate is expected to be equal to zero.

By implementing the fxed nominal exchange rate and assuming the ordinary wage rigidity associated with the long run equilibrium into a more complex AD function for a small open economy (see Sorensen & Jacobsen (2010) for complete derivation) implies:

(y − y) =

(e

+ ˇ

− ˇ) −

(i

− ˇ

− r

) + z (eq XI) It is also important to note that:

rt

e

+ (ˇ

− ˇ) = e (eq XII)

Since it is assumed that the regime is credible, the impact on ( 1) is naturally (e

) alone since the di˙erence in infation must be equal to zero. This implies that domestic producers output measured by the real exchange rate fuctuates positively with aggregate demand.

Infation expectations (e

) originate principally from two perspectives: one which treats expectations as static and one which treats expectations as weakly rational (forward-looking).

Neither is considered to be dominant in a theoretical setting and for the purpose of the model in treating infation expectations, it is prudent to formalize the idea that monetary policy is credible to the majority of agents that domestic infation is expected to follow foreign infation that will act as an informal infation target.

ˇ

= ˇ

= ˇ

(eq XIII)

With this regime the central bank is constrained and cannot regulate domestic infation other than anchoring its nominal exchange rate to a low-infation currency, also known as

“importing” infation, which could be expressed as an intermediate targeting regime. The

domestic economy is now susceptible to nominal shocks in the form of foreign infation of

which the domestic central bank cannot address without harming its own credibility. The

domestic economy is also at the mercy of previously mentioned speculative attacks. Should

however, the assumption of perfect capital mobility be relaxed and instead assume capital

controls, i.e. capital in and outfows are regulated. Using the nominal exchange rate as an anchor becomes a possibility, as capital fows no longer require the central bank to exhaust its foreign currency reserves in the event of nominal interest rate disparity. Additionally, by keeping the nominal exchange rate fxed international trade could beneft as calculations and contracts would be simplifed and be perceived as more secure for future transactions.

It should be noted that implementation and maintaining of capital controls is cumbersome with signifcant economic costs in practice.

Consider instead that the central bank pursues a free foating regime allowing independent monetary policy. Assuming monetary policy is aimed at infation targeting, agents in the market would perceive that the infation target will be equal to the average infation rate in the long term. Note the similarity of the assumption compared to the credible commitment to a fxed nominal exchange rate. We can formulate these expectations as:

ˇ

= ˇ

= ˇ

= ˇ

(eq XIV)

Which comprehensively describes the link of the central banks infation target and its credi- bility to the expectations of weakly rational agents in the market. In the absence of a credible fxed exchange rate target, agents will form new expectations regarding the level of the real exchange rate. Since they cannot forecast this accurately, their expectations will be static in nature. If the exchange rate is perceived by agents as deviating in either direction, it will normalize to the perceived normal level:

(e

− e

) = (e

− e

)  > 0 (eq XV)

Approximating the agents expectations on the latest observations and rewriting the previous equation:

e

= (e

e

− e) =  − (e − e

) (eq XVI) It follows from the UIP (eq I) that:

e = (e − e

) = −

(i − i

) (eq XVII)

Combining the UIP and static expectations of agents gives a modifed AD function:

(y − y) =

(e

− 

(i − i

) + ˇ

− ˇ) +

(i − i

+ r

− r

) + z (eq XVIII)

−

(i − i

) = exchange rate channel (i − i

) = interest rate channel

Note that monetary policy will a˙ect the AD function through two di˙erent channels under this regime. The exchange rate channel will respond to changes in the nominal interest rate between domestic and foreign currencies, a˙ecting competitiveness and net exports. The interest rate channel a˙ects private investment and consumption.

Continuing with the assumption that the central bank actively pursues an infation target, it follows that given:

ˇ

= ˇ

and ˇ

= ˇ

= ˇ

= ˇ

-> i = r

+ ˇ

+ h(ˇ − ˇ

) -> i − i

= h(ˇ − ˇ

) (eq XIX) Substituting into and rearranging the AD function gives:

(y − y) =

e

− ˆ

1

(ˇ − ˇ

) + z (eq XXII)

ˆ

=

+ h(

+ 

) (eq XXIII)

z =

(r

− r

) +

(g − g) +

(y

− y

) +

(ln − ln) (eq XXIV) Superfcially, both exchange rate regimes exhibit the same AD function. Nonetheless, several important underlying di˙erences need to be considered.

Assuming a fexible regime, an active monetary policy regime can theoretically considerably dampen supply shocks with with some fuctuations in output. Demand shocks can theoret- ically be signifcantly dampened to keep output and domestic infation reasonably stable.

For a fxed regime, with fnite foreign currency reserves logic would suggest a currency peg with a stable low infation economy. The specifc goal, observed outcome and instruments of monetary policy should dictate the choice of monetary policy regime, its degree of activity or passivity and the specifc instrument parameter may also impact what type of monetary policy regime is in e˙ect.

3,3 Central bank loss function with limited information.

Similar to the assumptions of the central bank in the AS-AD framework, the knowledge of the

central bank is limited and both demand and supply shocks cannot be forecast or observed

directly (referred to as the inside lag). Thus, expected values and covariances of shocks will

be zero and be independently distributed. Given that the central bank is independent and has been given the goal of maintaining price stability through an infation target (ˇ

). The central bank thus has no real preferences outside its given goal of infation targeting. Due to the delayed response of monetary policy (the outside lag) on real macroeconomic variables, the central bank sets nominal interest rate policy in advance so as to minimize any loss in future periods with the exact period depending on the time horizon of monetary policy (usually two years). The social loss function for period (j) to minimize can be theorized as:

SL

=

(ˇ

− ˇ

)

(eq XXV)

By employing equations VI and VII it is possible to discern the e˙ect when only minimizing infation in the social loss function. Given that time indexes move forward in both equations:

ˇ

= ˇ

+ (y

− y) + S

(eq XXVI)

For a central bank only concerned with infation given their objective, loss function and inability to observe shocks at time (t) in equation XIV, the best infationary forecast reduces to:

ˇ

= ˇ

+ (y

− y) − a2(i

− ˇ

− r

) (eq XXVII) Where (ˇ

) is the forecasted infation for two or more periods ahead by the central bank.

The output gap is present in calculating future infation, it bears no weight in the social loss function as the central bank retains a single objective when minimizing its loss function. As perfect information is not available, the central bank is subject to changes in the economic structure when minimizing its loss function which may contribute to regime switches as new information becomes available. This also applies to what parameters are included in forecasting the future infation, which will impact policy instrument choice and thus regime.

An active/passive regime targeting e.g. the exchange rate or infation may transition if the regime goal necessitates it and/or information allows it.

3,4 The Taylor Rule and the Lucas critique.

Since Taylor’s contribution of the popular monetary policy rule, possible revisions and criti-

cism have produced debate regarding specifcations, practical implementation of Taylor rule

estimations and assumptions made. Economists have debated whether the weights should be determined di˙erently and with what magnitude. E.g. a conservative central bank would put a larger weight on the infation gap than on the output gap, signaling a more strict infa- tion targeting monetary policy regime. In its original form the rule is static, with previous infation serving as expected infation for the coming time period. Taylors original paper also discusses the case of a fxed exchange rate regime with a Taylor rule, under which a

“world” nominal rate would be needed, since monetary policy is no longer independent and infation targeting is not viable.

The critique by Lucas (1976) argues that structural models of macroeconomics may be misleading, when parameters of the models fail to capture changing underlying factors. The simplicity of models such as the Taylor rule and relying on historical data, may provide misleading outcomes if changes in the microfoundations are ignored. Agents expectations and behaviour is unlikely to remain unaltered if and when policy change/become less active.

Expectations of infation and economic conditions by agents will impact policy and implicitly

the outcome the model will produce vis a vis the reality (accuracy of forecasts). The principal

of Lucas’ argument is related to the fact that parameters in the model may implicitly depend

on the policy regime at the time of measurement (Lucas, 1976).

4 Methodologies & Data.

4,1 Time-varying state-space model.

A generalized state-space model can be described as a dynamic system of equations, one describing the state of the system and one describing observations associated with that sys- tem (Durbin and Koopman, 2014). The unobserved/hidden state vector and the observable vector are separate and evolve independently, meaning observations of the system do not infuence the state of said system at any point in time. More precisely, observation variables at time (t) are independent of and do not infuence the entire state system given the state variables at time (t), but depend on the state of the system in question.

The variables of the state equation are assumed to evolve according to a markovian process, where observations of the state system contain “noise” distorting measurements in terms of errors. By observing the visible and relevant stochastic processes of observable variables, it is possible to make inference of the properties of the state variable based on the observed knowledge of the observed outcome variables which are linearly dependent on the state variables.

A simple time varying state-space model can be formalized in the following way, with (M ) state variables and (N ) observable variables:

y

= Ax

+ Bv

Observation equation x

= Cx

+ Dw

State equation

The observation equation displays the observable vector (y

) measured as a function of both the unobserved variable (x

) as well as an error term, note that the measurement of variable (y

) is “noisy” given the error term. It is assumed that (x

) follows a random walk with no seasonal present, this implies that (y

) and (x

) distributions are dependent on (t). Should this process be stationary, the solution would be straight forward analytically. The state question shows that the state of the system is dependent on its previous state as well as a stochastic process of (w

), where the state variable is assumed to follow an AR(p) process.

The coeÿcients of (A) and (B) are fxed system matrices of order (N ×m) and (N ×r), where

r = the dimensions of the disturbance vector in the observation equation. In a multivariate setting such as this paper, the system matrix (A) contains the independent variables.

Furthermore, the coeÿcients of (C) and (D) are also fxed system matrices of order (m × m) and (N ×g), where again (g) = the dimensions of the disturbance vector in the state equation.

The error terms (v

and w

) are assumed to be serially uncorrelated over time, with means of zero and with independent and unknown covariance matrices. Where (v

) and (w

) are (r × 1) and (g × 1) vectors respectively. Furthermore, it is assumed that (B, C, D, v, w) are unknown and need to be estimated. For the purpose of simplicity and derivation of the recursive procedure here, the errors are assumed to be normally distributed. Since the purpose of this paper is not to solve this problem analytically and neither to produce forecasts, the stationarity of the variables are not considered for the estimation procedure in the subsequent SS-model (Tanizaki, 1996).

4,2 The Kalman Filter.

The Kalman flter developed by Kalman (1960) involves a two stage process where the unobserved variable can be estimated given the observable data and its error through the construction of a likelihood function (Pichler, 2007). Employing the above assumptions, that the system is linear and that errors follow a normal probability distribution, the process uses a recursive prediction and correction approach. For full derivations of steps, likelihood function and complete discussion see Kalman 1960.

Assuming that possible values of the model parameters are known and equal to

  

(A

, B

, v , w

) and can be summarized by (A

, B

, v , w = ) . Using Bayes theo- rem and letting the likelihood function associated with the model and given parameters be denoted as:

QT t−1

;

f (y

, y

....y

; ) =

f (y|y ) (eq I)

where y

= (y

, y

...y

) for all t >= 2 (eq 11) Gives the likelihood function that are to be maximized:

QT

lnL(y

) =

lnf (y|y

; ) (eq III)

The prediction stage begins with the derivation of the initial state z

|

and an estimate of the related covariance matrix

= E[(z

− z

)(z

− z

)]. In this example it is assumed that this process is stationary, however this is not a requirement unless the flter operation is to solve a specifc equation. Setting t = 1 giving:

(x

) and

1

with the transition equation

x P

x

= Cx

and

C´ +

It follows that (x

) can then be used to construct a forecast of y

= Ax

given that we can observe the dependent variable in the observation equation. It also allows for the forecast error to be constructed according to:

u

= y

− y

= y

− Ax

= v

+ A(x

− x

) (eq IV) Given that: y

= u

+ y

leads to f (y

|y

; ) = f (u

; )

Based on previous states and error terms, current states and error terms have been produced by (x

) and

but in order to construct future state values we need the current values of x

and

.

Since we have observed the current value of (y

) it is possible to correct the previous predic- tions of (x

) and

according to Kalman (1960) formula:

x

= x

+ K

(y

− y

) = x

+ K

(y

− Ax

) (eq V)

Px_t|t−1

=

−K

(

+A

A´)K

(eq VI)

P x P P v

)

Where: K

=

A´(A

A´ + (eq VII)

Combining the previous prediction of the state and the current prediction of the error in (y

) it is possible to construct a linear corrected prediction of the unobserved state variable.

Furthermore, due to the linearity, the choice of (K

) is to minimize the variance in the prediction error.

This prediction and correction procedure is done recursively until (t = T ). When this point is reached the likelihood function can be constructed by the known model parameters according to:

T QT t−1

;

ln(y , ) =

f (y|y )

Producing smoothed and fltered states of the estimated model. The prediction fltered states gives the distribution of the current (post estimate) state given the observations up to and including the current time index. The smoothed states gives the distribution of past state/states, given the data up to the current time index, where the latter is to be employed in this paper.

4,3 Autoregressive Hidden Markov Switching model.

In the feld of economics, statistics and fnance time series analysis is commonly plagued by the presence of structural breaks in the underlying data. This can generally cause problems with linear and non-linear estimators that may become unreliable given the non-stationarity (Hamilton, 2005). This usually represents events that dramatically change the behaviour of the data, e.g. new governmental policy or market condition that respond to a fundamental change in its environment, such as a fnancial crisis. However, these fundamental changes provide a point of inquiry for the underlying cause of these changes in regimes, that cannot be directly observed, but is present in the data.

By employing the modelling developed by Hamilton (2005), consider the time series variable (y

) which can be modeled according to an autoregressive process described as:

y

= aR

+ y

+ 

With  ˘ N (0, ˙

) for all t >= 1

Where (R

) denotes the state variable which behaves as a stochastic variable that is the result of an exogenous change. Should a simple replacement of the constant term (a), then representing a signifcant change in the average of the time series, provide an improvement in the estimate of (y

), it would be considered a deterministic change clearly visible and thus completely predictable (Hamilton, 2005). The state variable (R

) captures these imperfectly predictable changes in the time series without assuming that they are deterministic and thus visible. The state variable is assumed to change over time and assume values of:

R

= 1 for t = 1, 2, , , , , t

and R

= 2 for t = t

+ t1, t

+ t2, , , , ,

In order to describe the behaviour of (R

) moving from one state/regime to another, a

probabilistic model is required. A natural way of accomplishing this is to model the state of

(y

) as a markov chain of probabilities. Continuing with the simplicity of a two state markov chain:

P r(R

= j|R

= i, R

= k, , , y

, y

) (eq VIII)

= P r(R

= j|R

= i) = p

(eq IX)

Intuitively, this Markov chain of probabilities relies on past values and is autoregressive, with an emphasis on the values of the most recent state/regime. Meaning that several di˙erent regimes may exist and transition between said states occurs, such transitions are infrequent and considerable time may pass between transitions. The degree of permanence of the regime or state is represented by the value of (pij). Which denotes the probability of transitioning from one state to another or remaining in the current state, represented as a probability matrix with its size equal to the number of states in the model.

This constitutes an Autoregressive Hidden Markov Switching Model, which allows for the parameters to vary across regimes and can be viewed as an unrestricted model with initially

“hidden” or unobservable regimes. The regimes evolve exogenously of the time series in question and the dimension primarily depends on theoretical considerations of the underlying data as well as calculation restrictions. Similarly to the dynamic linear system model in the previous section, the states cannot be observed directly/are “hidden”. However, the parameters of the model allow for inference of the probability of states within the model.

4,4 Data collection and management.

The dependent column vector consists of the BOBUR, which is the three month interbank

rate of Hungary issued by the central bank of Hungary (MNB, 2020). The interbank rate is

issued monthly or minimum once per quarter depending on the need for adjustment decided

by the Monetary Council (MNB, 2020). This data vector has been collected from the OECD

database of main economic indicators reported in percentages, which are not seasonally

adjusted. Harmonization of data points was achieved by taking the geometric mean for every

quarter in absolute percentages points. This also ensures gaps in the data are eliminated,

e.g. if a single rate is issued in a quarter it automatically becomes that quarters geometric

average.

The choice of the three month interbank rate rather than e.g. the one year government bond rate, is based on the direct impact on the banking system by central bank intervention and its relation to monetary policy. Other measurements such as the governmental bond rate present issues of rating of bonds, impact of pension funds and time of issuance for data collection.

The independent column vector of infation consists of consumer price index (CPI) adjusted for food and energy, i.e. core infation for Hungary measured quarterly as the annual growth rate from the previous period in percentages. The base year for the infation measurement is 2015, is not seasonally adjusted, based on a fxed set of consumer goods and services in fxed quantities and weighted according to a large number of elementary aggregate indices (OECD, 2020). This data vector has been collected from the OECD database of main economic indicators. As infation has been highly unstable in former soviet occupied countries, the choice of using core infation provides more stable data with less outliers.

Naturally, the column vector of target infation is derived from the published reports of the MNB monetary Council, with the introduction of explicit infation targeting with reference date December 2001 (MNB, 2020). Prior to this date managing price stability was the primary goal of the MNB, but not its sole goal. Aspiring entrance into the EMU was still pursued ex ante and ex post adoption of infation targeting. As these two goals may not be fully compatible the MNB elected to let their currency foat beginning in 2008 with infation target adjustments being made every three to fve years conditional on infation forecasts and their realizations (MNB, 2020).

The independent column vector of output consists of real Gross Domestic Product for Hun- gary measured in millions of Hungarian national currency (Forint), reports are issued quar- terly and being seasonally adjusted. The data for this vector has been collected from the OECD database of main economic indicators (OECD, 2020). Other measures of deviations from potential output, such as unemployment deviation from the NAIRU are not considered in this paper.

In addition, the Real E˙ective Exchange Rate (REER) is added to the open economy model.

The REER adds an additional channel of transmission for monetary policy, as a potential intermediate target variable of MNB (Svensson, 2000). The REER consists of the real exchange rate of the Hungarian currency Forint against a basket of sixty economies weighted and indexed according to the size of trade with each basket country. The REER are derived as geometric weighted averages of bilateral exchange rates adjusted by consumer prices, reported monthly (BIS, 2020). Weights are derived from manufacturing trade fows with a time varying pattern, with weights being recalculated as recently as 2014-2016 (ibid), collected from the Bank of International Settlements (BIS).

As with harmonizing the BOBUR, the monthly data points are converted to a geometric mean for all quarters in absolute percentage points. The choice of measurement being the weighted and indexed REER, is guided by the desire to capture changes in the real exchange rate in consideration of the major trading partners of Hungary. Rather than simply taking into account the largest one, the Euro area, thus capturing a wider relationship to Hungarian monetary policy.

Both models require the same basic variable construction and are estimated in R using the MSWM (Markov Switching model) and KFAS (Dynamic Linear System Model) packages respectively.

Constructing the defnition of the infation gap was accomplished by subtracting the infation

target from the actual measure of core infation. Data points in the infation target vector

prior to the introduction of infation targeting was set to zero, making the infation gap equal

the core infation (Kuzin, 2004). The output gap is defned by decomposing the real GDP

using the Hodrick Prescott flter, to extract the trend and cyclical components respectively

with the customary penalizing agent of  = 1600 for quarterly data (Hodrick and Prescott,

1997). The resulting trend component was then used as the denominator when taking the

quotient of the natural log of real GDP and natural log of the trend component, multiplied

by 100 for scaling. This procedure was repeated for the Forint REER indices, producing a

REER gap of the actual indices for the basket of economies and the trend level of REER for

said basket.

4,5 Autoregressive Hidden Markov Model.

The HMM estimation procedure, described above, requires that a gaussian linear model is estimated with the associated characteristics of OLS. After which the expectation- maximization (or EM) algorithm is applied to the defned gaussian linear model through the MSWM package.

One additional regressor is included in the form of a lagged dependent variable, this is due to strong autocorrelation of the residuals in the error term (t). This e˙ect is referred to as interest rate smoothing (Clarida, Gali, Gertler, 1998), capturing the tendency of cen- tral banks maintain momentum in changes of the nominal interest rate. The coeÿcient of the lagged interest rate determines the degree of interest rate smoothing, with the term ˆ =

= ˆ

represents a persistence measure. Unit root and Stationarity tests for all gap variables were conducted according to the Augmented Dickey Fuller (ADF) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests. The ADF unit root test indicates a pos- itive unit root in BOBUR only (see Appendix). The KPSS test indicates that all variables are trend stationary with non-rejected nulls for all variables. Breakage-tests with unknown breakage points were conducted on all variables where the infation gap exhibited two breaks in 2002 and 2010, and the BOBUR exhibited breaks in 2004, 2009, 2012 and 2017.

Determining the AR(p) component of the HMM employed both Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were calculated for up to ten lags of each independent variable. Results of these tests were inconclusive and not pursued. Furthermore, a Partial Autocorrelation Function (PACF) was employed to determine the number of lags of each dependent variable with a maximum of fve lags. The results for both the infation and output gap variable suggest a lag length of one, The REER gap shows signs of seasonality with lag indications every three lags, consistent with a seasonal pattern of one per year.

Extended PCAF tests with a maximum of thirty lags rejected the hypothesis of a seasonal component in REER. The REER gap was estimated with a zero lag length. Furthermore, the intercept does not produce any meaningful result as it is likely not a constant and conditional on fuctuations in the Wicksellian rate of interest (Woodford, 2001).

The number of regimes estimated is empirically indicated to be three; one per independent

variable, excluding the lagged nominal rate. In the estimation process a three state regime was rejected on the basis that the model estimation matrix approaches singularity. Instead a two regime autoregressive model with time varying coeÿcients was estimated according to:

(i

− i

) =

(ˇ

− ˇ

) +

(y

− y

) +

(ˆ

− ˆ

)(1 − ˆ) + i

+ 

(eq X) Where: i

= BOBUR at time t, (ˇ

− ˇ

) = infation gap at time t, (y

− y

) = output gap at time t, (ˆ

− ˆ

) = REER gap at time t, i

= interest rate smoothing, 

= error term at time t.

4,6 State-Space Model.

The state space model estimated di˙ers from the HMM in that the autoregressive element of interest rate smoothing was omitted on the basis that it did not add anything qualitatively to the results. Such a model was estimated in line with the autocorrelation argument but did not a˙ect the coeÿcients in any meaningful manner, only increasing the parametrization of the model. Disturbance matrices were specifed with each state having an initial inherent disturbance (o˙-diagonal elements equal to zero) and covariances. Allowing the smoothing algorithm to estimate appropriate initial values for all state vectors, where all independent state vectors were assumed to follow a random walk without a drift. The variation in the model is exclusive to the level of the weights and not the variables in their entirety. Again the intercept is excluded in order to keep the model identifable and not add an additional disturbance term (Helske, 2016). The estimated model is thus:

i

=

(ˇ

− ˇ

) +

(y

− yt

) +

(ˆ

− ˆ

) + 

(eq XI)

5 Empirical Results & Discussion

5,1 Empirical Results

With Kalman flter results, traditional numeric output tables would serve no purpose in the context of mediating any results produced by the Kalman flter. As coeÿcients vary across time a graphical representation is a more appropriate setting for demonstrating the estimates of the modifed Taylor rule. Each smooth estimate can be described as the expectation conditional on the nominal rate and other structural parameters, or more formally E[

|i

, ] . The smooth estimates of variables displayed as continuous lines with 95% confdence intervals calculated as standard ± 2RMSE of each individual smoothed state estimate.

−4 0 4

Betas Inflation gap 2000−Q1 2002−Q2 2004−Q4 2007−Q2 2009−Q4 2012−Q2 2014−Q4 2017−Q2 2019−Q4

Figure 1: Infation gap estimate including confdence intervals

Comparing the nominal rate and the estimate of the infation gap in Figure 1 indicates

movements consistent with a central bank responding to deviations from the target infation

during the frst half of the sample, with a strong emphasis on positive deviations. Signifcant

negative infation gap coeÿcients are rare but occur at three peaks in 2005, between 2010-

2011 and in 2014. Excluding 2010-2011, they fairly immediately return to non negative

weights. The majority of the time period exhibits fairly large weights on the infation gap

as prescribed by the Taylor rule. Ranging from consistent weights in the vicinity of 1-2,

well above unity, and in some circumstances up to weights between 3-4. This is particularly noticeable during the peaks of 2004 and 2009, indicating a active conservative central bank prioritizing anti infationary tendencies which are consistent with the lagged monetary policy enacted with infation targeting. The end half of the sample exhibits more instability in the commitment to positive weights for the infation gap, as the monetary policy regime allows for more persistent negative weights during 2008-2017, indicating a more passive Taylor rule.

−4 0 4

Betas Output gap 2000−Q1 2002−Q2 2004−Q4 2007−Q2 2009−Q4 2012−Q2 2014−Q4 2017−Q2 2019−Q4

Figure 2: Output gap estimate including confdence intervals

The coeÿcients of the output gap in Figure 2 displays similar irregularities as the infation gap at certain intervals. Initial fairly large positive weights on the output gap indicates emphasis on economic growth and an active monetary policy regime, particularly during the mid 2000s. A consistent negative weight is observed during the fnancial crises in the vicinity of 2008, recovery to expected positive weights of 1-2 is slow. Comparing weights of the infation and output gasp, the latter tracks as reversed, e.g. in 2005. Suggesting that monetary policy prioritizing the weight of the infation gap subtract from the weight put on the output gap in a procyclical manner, similar to Tarkhan-Mouravi (2009). Although, this e˙ect appears to be alternating as this is not consistent, e.g. weights in 2004 are tremendously positive for both gaps respectively. Similar to the infation gap, the frst half of the sample pre-2008 indicates activist monetary policy, with passivity after 2008.

Compared to both output and infation gaps, the REER gap estimates in Figure 3 exhibits